Related papers: Finding Dantzig selectors with a proximity operato…
Dantzig's vertex pivot simplex method has been published for more than seven decades. Amazingly, it remains one of the most efficient methods to solve linear programming (LP) problem after numerous efforts trying to find some better…
This paper studies proximal gradient iterations for solving simple bilevel optimization problems where both the upper and the lower level cost functions are split as the sum of differentiable and (possibly nonsmooth) proximable functions.…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
We study the problem of detecting change points (CPs) that are characterized by a subset of dimensions in a multi-dimensional sequence. A method for detecting those CPs can be formulated as a two-stage method: one for selecting relevant…
We report on progress in algorithms for iterative phase retrieval. The theory of convex optimization is used to develop and to gain insight into counterparts for the nonconvex problem of phase retrieval. We propose a relaxation of averaged…
Object detection is a basic computer vision task to loccalize and categorize objects in a given image. Most state-of-the-art detection methods utilize a fixed number of proposals as an intermediate representation of object candidates, which…
A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…
This work deals with the a posteriori error estimates for the Darcy-Forchheimer problem. We introduce the corresponding variational formulation and discretize it by using the finite-element method. A posteriori error estimate with two types…
Gradient-based methods are well-suited for derivative-free optimization (DFO), where finite-difference (FD) estimates are commonly used as gradient surrogates. Traditional stochastic approximation methods, such as Kiefer-Wolfowitz (KW) and…
In this paper we study the convergence of an iterative algorithm for finding zeros with constraints for not necessarily monotone set-valued operators in a reflexive Banach space. This algorithm, which we call the proximal-projection method…
We present a class of iterative fully distributed fixed point methods to solve a system of linear equations, such that each agent in the network holds one of the equations of the system. Under a generic directed, strongly connected network,…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…
We consider the reconstruction of moving sources using partial measured data. A two-step deterministic-statistical approach is proposed. In the first step, an approximate direct sampling method is developed to obtain the locations of the…
Solving linear systems is a ubiquitous task in science and engineering. Because directly inverting a large-scale linear system can be computationally expensive, iterative algorithms are often used to numerically find the inverse. To…
The problem of synthesizing an optimal sensor selection policy is pertinent to a variety of engineering applications ranging from event detection to autonomous navigation. We consider such a synthesis problem over an infinite time horizon…
Spatially localized structures are key components of turbulence and other spatio-temporally chaotic systems. From a dynamical systems viewpoint, it is desirable to obtain corresponding exact solutions, though their existence is not…
We consider the dynamic linear regression problem, where the predictor vector may vary with time. This problem can be modeled as a linear dynamical system, with non-constant observation operator, where the parameters that need to be learned…
A method to calculate the adjoint solution for a large class of partial differential equations is discussed. It differs from the known continuous and discrete adjoint, including automatic differentiation. Thus, it represents an alternative,…
In this paper, we propose an algorithm combining the forward-backward splitting method and the alternative projection method for solving the system of splitting inclusion problem. We want to find a point in the interception of a finite…